Weak Mixing of Random Walks on Groups

Let G be a locally compact -compact group with right Haar measure m and a regular probability measure on G. We say that is weakly mixing if for all gL (G) and all fL ¹(G) with fdm=0 we have n ^{–1 n} _k=1| ^k *f,g|0. We show that is weakly mixing if and only if is ergodic and strictly aperiodic. To prove this we use and prove some results about unimodular eigenvalues for general Markov operators.     

Truncated diastereoselective Passerini reaction, a rapid construction of polysubstituted oxazole and peptides having an α-hydroxy-β-amino acid component

The reaction of aldehydes and ketones, including aliphatic and aromatic ones, with amides of α-isocyano-β-phenylpropionic acid in toluene in the presence of lithium bromide gives 2,4,5-trisubstituted oxazoles in good to excellent yield. Protected chiral α-amino aldehydes participate in this reaction to give, after hydrolysis of the oxazoles, norstatine-containing peptides in good overall yield. The nucleophilic addition of isonitriles to N,N-dibenzylphenylalanal is investigated for the first time and is found to be stereoselective leading predominantly to the anti-adduct (dr=9/1). On the other hand, the reaction between the N-Boc phenylalanal and isonitrile is non-stereoselective.     

Benzologs of allopurinol: Synthesis of pyrazolo [4,3-g] and [3,4-f] quinazolinones

Convenient syntheses of pyrazolo [4,3-g]quinazolin-5 (6H) -one (3), its xanthine oxidase metabolite 4 and the [3,4-f] analog 5 have been developed, involving anellation of the pyrimidine ring onto aminoindazolcarboxylic acids 9 and 18, or attachment of the pyrazol portion onto quinazolinone 22 via intramolecular azo coupling.     

Permeabilite selective et solvatation preferentielle

Experimental data concerning the preferential solvation displayed by polyvinylpyrrolidone (PVP) dissolved in various mixed solvents are compared with the selectivity observed when a membrane, prepared by grafting vinylpyrrolidone into a thin film of polytetrafluoroethylene, is used to fractionate the same binary liquid mixtures by pervaporation. The investigation systems are:—ethanol/1,2- dichloroethane, ethanol/chloroform and acetic acid/1,2- dichloroethane. A close correlation is found between the two phenomena. The component which, in solution, is preferentially sorbed by polyvinylpyrrolidone, diffuses more readily through the PTFE-PVP membrane. When an inversion occurs, at a given concentration, in the preferential solvation, an inversion of selectivity is also observed in pervaporation at the same feed liquid composition.     

Defining Cdk5 ligand chemical space with small molecule inhibitors of tau phosphorylation

Cyclin-dependent kinase 5 (Cdk5) is widely viewed as a possible target for a wide variety of neurological disorders. One pathological role attributed to Cdk5 is the abnormal phosphorylation of tau that may lead to the neuronal inclusions known as neurofibrillary tangles. A high through-put screen for inhibitors of Cdk5-mediated phosphorylation of tau resulted in three compounds with distinct mechanisms of action. One compound is competitive with ATP and has a high affinity for the Cdk5 ATP binding pocket. The second compound also competes with ATP, is noncompetitive with tau, and (uniquely among this class of inhibitors) displaces adjacent amino acid residues to make room for the nitrophenyl group. A third compound did not compete with ATP, but did compete with tau at low concentrations of tau. The SAR and charge optimization derived from cocrystals of the two ATP competitors along with cocrystals of three other ATP competitors map out the importance of filling and properly charging different regions of the ATP binding pocket. Taken together, this analysis shows how the structure of Cdk5 constrains the space of potential inhibitors and reveals a pocket unfilled in all of the structures. These leads could be a starting point for structure-based drug design of more potent and selective inhibitors.